Extensional schemes of multipartite non-interactive key exchange from multilinear maps and their applications

摘要

The question of generalising the celebrated 2-party non-interactive key exchange ( NIKE ), Diffie-Hellman protocol, to a multipartite setting was left as an important open problem. In 2003, Boneh and Silverberg put forward a theoretical construction of multipartite NIKE protocol from a new notion called multilinear maps. In their protocol, however, the number of users N and the multilinearity k are related by N = k + 1, resulting in the system initialising another multilinear map when the number of users who want to exchange a session key changes. In this paper, we describe two extensional schemes of multipartite NIKE, which enables any less than or equal to N users derive a common shared key from an ( N – 1)-multilinear map. In addition, using our extensional schemes, we show a concrete scenario: the establishment of any discussion group in a user group and its privacy version. Furthermore, we analyse its security.